Math 302: Applications and Numerical
Solution of Ordinary Differential Equations
http://www4.ncsu.edu/eos/users/w/white/www/white/ma302/ma302hp08.htm
NCSU
Statement on Disability and Honesty
Instructor: ??, Fall 2008
This
course uses Matlab, Matlab's ODE
suite, and is taught at a level suitable for students who have passed two
semesters of calculus. There are five parts, and each has three lectures. The
first lecture introduces a new topic, and the following two lectures will
stress applications and variation of the model's parameters. Additional
course materials can be found in the texts by Danby, or Nagle, Saff and Snider.
Grading
and Exam Dates
Matlab
m-Files
Part I: First Order ODE and Euler Methods
1.
Matlab (plot, function, loop, m-files), y(t) = 70 +130e-kt
2.
Falling mass, Euler and improved Euler methods
3.
Cooling with variable ambient temperature, variable time steps
Part II: Logistic ODE and Higher Order Methods
4.
Population,
5.
Population with harvesting, ODE45
6.
Spread of information, ODE45
Part III: Higher Order Systems
7.
Predator-prey(s), ODE45
8.
SIR Epidemic model, ODE45
9.
Diffusion of Heat (discrete rod), ODE45
Part IV: Vibration and Resonance
10.
Mass-spring and resonance, ODE45
11.
Vibrating string (discrete string),
ODE45
12.
LRC circuit and tuning, ODE45
Part V: Stiff Systems
13.
Rapid cooling, Euler-trapezoid, ODE23s
14.
Van der Pol circuits, ODE23s
15. Oregonator chemical reactions, ODE15s